literature - Literary device: frequently referenced object which never appears

They are often referred to as "off-stage characters" (or off-stage objects, places, etc.). This is even the case in media such as novels or radio plays that don't have a stage (using the mechanics of theatre as a source of metaphors for those other media).

Godot is a slightly more complicated case, because it's not clear whether he even exists, depending on how you interpret it, though it would still apply.

Sometimes even objects that aren't people are referred to as "off-stage characters" because they have such a strong impact upon the narrative. There's a clear degree of metaphor being used here, but it's not uncommon to find people talking about "the sea as an off-stage character" and so on.

Some people have suggested MacGuffin. A MacGuffin is something that drives the plot in some way, and hence clearly has some significance to the characters, but has no significance beyond that. A MacGuffin could be off-scene for all of a story, could be obtained at the end, or could be with the protagonist for the entire story (Goody McGooderson must travel across war-torn Ruritania with the MacGuffin, keeping it from Evil McEvilson and his network of spies). If you could change the MacGuffin for someone else (swap out "enemy codes" with "enemy weapon plans" or "diamonds" for "drugs") and have the same story, it's a MacGuffin. Otherwise you can't.

Godot is a MacGuffin in some interpretations of the play, and not in some others, as whether the question of who or what Godot is is even important differs with those interpretations. If you consider the question as unimportant, then you believe Godot is a MacGuffin.